a quantitative analysis of the impact of wind turbines on operational doppler weather radar data

In order to eval-uate the impact of the wind farm, average values of all three spectral moments the radar reflectivity factor, absolute radial velocity, and spectrum width of the nearby

doi:10.5194/amt-8-593-2015

© Author(s) 2015 CC Attribution 3.0 License

A quantitative analysis of the impact of wind turbines on

operational Doppler weather radar data

L Norin

Atmospheric Remote Sensing Unit, Research Department, Swedish Meteorological and Hydrological Institute,

Norrköping, Sweden

Correspondence to: L Norin (lars.norin@smhi.se)

Received: 26 July 2014 – Published in Atmos Meas Tech Discuss.: 27 August 2014

Revised: 9 January 2015 – Accepted: 10 January 2015 – Published: 5 February 2015

Abstract In many countries wind turbines are rapidly

grow-ing in numbers as the demand for energy from renewable

sources increases The continued deployment of wind

tur-bines can, however, be problematic for many radar systems,

which are easily disturbed by turbines located in the radar

line of sight Wind turbines situated in the vicinity of Doppler

weather radars can lead to erroneous precipitation estimates

as well as to inaccurate wind and turbulence measurements

This paper presents a quantitative analysis of the impact of

a wind farm, located in southeastern Sweden, on

measure-ments from a nearby Doppler weather radar The analysis is

based on 6 years of operational radar data In order to

eval-uate the impact of the wind farm, average values of all three

spectral moments (the radar reflectivity factor, absolute radial

velocity, and spectrum width) of the nearby Doppler weather

radar were calculated, using data before and after the

con-struction of the wind farm It is shown that all spectral

mo-ments, from a large area at and downrange from the wind

farm, were impacted by the wind turbines It was also found

that data from radar cells far above the wind farm (near 3 km

altitude) were affected by the wind farm It is shown that this

in part can be explained by detection by the radar sidelobes

and by scattering off increased levels of dust and turbulence

In a detailed analysis, using data from a single radar cell,

frequency distributions of all spectral moments were used to

study the competition between the weather signal and wind

turbine clutter It is shown that, when weather echoes give

rise to higher reflectivity values than those of the wind farm,

the negative impact of the wind turbines is greatly reduced

for all spectral moments

1 Introduction

As a response to the increasing demand for renewable en-ergy the number of wind turbines is growing rapidly in many countries around the world The worldwide installed cumula-tive energy capacity of wind turbines has shown a more-than-13-fold increase during 2001–2013 In Sweden, the wind power capacity has increased even more, 15 times, during the same period (Global Wind Energy Council, 2014) In the coming years many more wind turbines are expected to

be built and existing, older ones are likely to be replaced

by larger, next-generation turbines Modern wind turbines are large structures, many reaching 150 m above the ground Clusters of densely spaced wind turbines, so-called wind farms, are being built both on- and offshore

The continued deployment of wind turbines and wind farms presents a problem for many radar systems, which are easily disturbed by wind turbines located in the radar line

of sight Due to their rotating blades, interference caused by wind turbines is more severe for radar systems than inter-ference caused by stationary structures (e.g masts or tow-ers) Many Doppler radars use a clutter filter that suppresses echoes originating from objects with no or little radial veloc-ity, but such filters do not work for moving objects such as the rotating blades of a wind turbine It has been shown that wind turbines located in the line of sight of Doppler radars can have a detrimental impact on the performance of both military and civilian radar systems (see, e.g., Poupart, 2003; Department of Defense, 2006; Lemmon et al., 2008; Lute and Wieserman, 2011)

Doppler weather radars, employed by meteorological and hydrological services, can also be negatively affected by nearby wind turbines Weather radars are valuable tools for

monitoring precipitation and wind shear as well as for

ob-serving hazardous events such as hailstorms, heavy

rain-fall, and tornadoes Information from weather radars is also

used as input to numerical weather prediction and

flood-forecasting models Errors in weather radar data may

prop-agate to affect the output of such forecast systems (Rossa

et al., 2011)

Several studies dedicated to wind turbine impact on

weather radar data have presented images of radar

compos-ites that convincingly show that wind farms indeed can be

detected by weather radars (see, e.g., Burgess et al., 2008;

Crum and Ciardi, 2010; Vogt et al., 2011) In other studies,

time series of raw radar data have been recorded in order to

perform detailed analyses of the impact of wind turbines by

spectral analysis Gallardo et al (2008) collected raw radar

data over a few months from a Spanish C-band weather radar

to analyse the impact of a large wind farm, while Isom et al

(2009) used several hours’ worth of raw data from two US

S-band weather radars to investigate the same phenomenon

Toth et al (2011) used a mobile X-band Doppler radar to

study the impact of wind turbines from close range

How-ever, only a few analyses of wind turbine impact on long time

series of operational weather radar data have been published

(Haase et al., 2010; Norin and Haase, 2012)

The main objective of this study is to analyse the impact of

wind turbines on operational Doppler weather radar volume

data This study thus extends the work by Haase et al (2010)

and Norin and Haase (2012) In this study the wind turbine

impact on all three spectral moments (the radar reflectivity

factor, radial velocity, and spectrum width) have been

inves-tigated in order to improve the understanding of wind turbine

impact on Doppler weather radar data In total, 6 years’ worth

of operational polar volume data were used for the data

anal-ysis

The structure of the paper is as follows The technical

char-acteristics of the Swedish radars are described in Sect 2 The

radar data set together with the analysed wind farm are

pre-sented in Sect 3 In Sect 4.1 the impact of wind turbines on

data from a single radar scan is shown by comparing average

values of the spectral moments, before and after the

construc-tion of the wind farm In Sect 4.2 the wind turbine impact on

polar volume data is investigated Section 4.3 presents a

de-tailed analysis of the wind turbine impact on data from a

sin-gle radar cell, by examining frequency distributions for all

spectral moments as a function of reflectivity from a

refer-ence radar cell The competition between the weather

sig-nal and wind turbine clutter is investigated in Sect 4.4, and

in Sect 5 the impact of the wind farm on measurements far

above the radar is discussed Finally, in Sect 6, a summary of

the study is given and conclusions of the analyses are drawn

2 The Swedish weather radars

The Swedish weather radar network consists of 12 horizon-tally polarised Ericsson C-band Doppler radars, providing almost complete national coverage The radars perform az-imuthal scans of 360◦ around a vertical axis for 10 tilt an-gles, θ , ranging from θ = 0.5◦ to θ = 40◦ The antenna ro-tational speed is vr=2 rpm Together, these scans make up polar volume data sets which are provided with an update time of 15 min

The data processing is managed by the radar signal pro-cessor The four lowest scans (θ = 0.5◦ to θ = 2.0◦) use a different measurement strategy than the highest six scans (θ = 2.5◦to θ = 40.0◦) The received signal is digitised us-ing an 8 bit analogue-to-digital converter with a samplus-ing rate

of 0.9 (1.8) MHz for the lower (higher) scans, corresponding

to 167 (83) m range bins A radar cell consists of 12 range bins, and thus the range resolution for a radar cell is 2 (1) km for the lower (higher) scans The lower scans also use a lower set of pulse repetition frequencies (PRFs), 450 Hz or 600 Hz, whereas the higher tilt angles use a higher set of PRFs (900

or 1200 Hz)

For all scans the signal processor uses 32 measurements from each PRF to compute a Fourier transform, which means that the azimuthal resolution depends on the set

of PRFs For the lower scans the azimuthal resolution is 360/60/ vr(32/PRF1+32/PRF2) ≈ 1.49◦, whereas for the higher scans the azimuthal resolution is approximately 0.75◦ Data are, however, output in matrices consisting of

120 × 420 radar cells for every scan The apparent azimuthal resolution is thus 360/420 ≈ 0.86◦for all scans

The main radar lobe has a half-power beam width of 0.9◦ The first sidelobes appear at approximately 2.5◦near

−30 dB in the horizontal direction and at approximately 2◦ near −30 dB in the vertical direction (a vertical cut of the antenna pattern is shown in Sect 5)

Doppler weather radars measure three spectral moments (see, e.g., Doviak and Zrni´c, 2006): the radar reflectivity fac-tor (hereafter referred to as reflectivity), radial velocity, and spectrum width These spectral moments are used to estimate quantities such as precipitation rate, wind speed, and turbu-lence

Reflectivity, Z, is the power of the returned signal and

is measured by the radar in units of dBZ The mini-mum detectable signal of the Swedish radars is better than

−114 dBm Whenever the radar receives a signal stronger than the minimum detectable signal, a hit is recorded and converted to reflectivity The Swedish weather radars have

a dynamic range of > 85 dB and measure Z between −30 and 71.6 dBZ in steps of 0.4 dBZ The minimum value (−30 dBZ) represents all measurements ranging from −∞

to −30 dBZ Such values are classified as undetected mea-surements

Radial velocity, V , is obtained as the first moment of the power-normalised Doppler spectrum Two PRFs are used

al-Table 1 Selected characteristics of Swedish weather radars.

0.5◦, 1.0◦, 2.5◦, 4.0◦, 8.0◦, Tilt angles 1.5◦, 2.0◦ 14.0◦, 24.0◦, 40.0◦

Measurement radius 240 km 120 km

Azimuthal resolution 0.86◦ 0.86◦

Max unambiguous velocity 24 m s−1 48 m s−1

ternatively to allow real-time dealiasing of the radial

veloc-ities The maximum unambiguous velocity is ±24 m s−1for

the four lowest scans and ±48 m s−1for the six highest scans

The radial velocity resolution is 0.1875 m s−1 (0.375 m s−1

for the higher scans) Undetected reflectivity measurements

(Z ≤ −30 dBZ) result in unreliable estimates of radial

veloc-ity, and such measurements are therefore classified as

unde-tected

Spectrum width, W , is calculated as the square root of the

second moment about the first of the power-normalised

spec-trum The measurements of the spectrum width fall into one

of four classes: 0–1, 1–2, 2–3, and > 3 m s−1for the four

low-est scans and 0–2, 2–4, 4–6, and > 6 m s−1for the six highest

scans As for radial velocity, undetected reflectivity

measure-ments (Z ≤ −30 dBZ) result in unreliable estimates of

spec-trum width, and such measurements are therefore classified

as undetected

Invalid measurements are produced when the radar does

not perform correctly, such as when failing to find a requested

angle in azimuth or elevation or if the transmitter is not ready

in time Invalid measurements for any spectral moment are

given separate values by the radar

All radars in the network are equipped with clutter filters

which are used to suppress ground echoes The clutter filter is

turned on for all scans Ground echo suppression is obtained

by omitting amplitudes from the three frequency channels

closest to 0 in the frequency spectrum (channel 0, 1, and 31)

For the lowest four scans (using the lower set of PRFs) this

removes echoes with radial velocities less than ±1 m s−1; for

the highest six scans radial velocities with ±1.5 m s−1 are

omitted To protect the radar receiver from overload the

sig-nal is damped by 60 dB near the radar, making the data of the

first two rows of radar cells unusable

Relevant radar characteristics are summarised in Table 1

200 400 600

800

Figure 1 Schematic plot of the Brunsmo wind farm The positions

and heights of the wind turbines are shown together with the alti-tudes of the half-power beam width of the main radar lobe for the

3 Data set and wind turbines

Operational polar volume data from the Swedish weather radars are available from the year 2005 and later Some changes were made in the radar scan strategy as well as to the radar hardware during 2007, but from 2008 the radar scan strategy and measurement techniques have remained unal-tered Radar data from 2008 and later hence constitute a ho-mogeneous data set

In order to investigate the impact of wind turbines

on Doppler weather radar data, we have analysed opera-tional polar volume data from weather radar Karlskrona (56.2955◦N, 15.6103◦E) for a period of 6 years (1 Jan-uary 2008 to 31 December 2013) Throughout this period

no significant data gaps exist, and radar service records do not show any indication of radar malfunctioning occurring during this period

Brunsmo wind farm is located in southeastern Sweden, ap-proximately 13 km northeast of weather radar Karlskrona This wind farm consists of five General Electric 2.5 MW wind turbines with total heights of 150 m above the ground These wind turbines have a rotor diameter of 100 m, a

cut-in wcut-ind speed of 3.5 m s−1, and a cut-out wind speed of

25 m s−1 The wind turbines were erected in October and Novem-ber 2009, and the wind farm became operational in April 2010 The proximity of the Brunsmo wind farm to weather radar Karlskrona together with the date of the wind farm’s start of operations (near the middle of the homoge-neous radar data set) makes the Brunsmo wind farm well suited for a detailed study

Figure 1 shows a schematic picture of the locations and heights of the wind turbines of the Brunsmo wind farm to-gether with the altitudes of the radar lobes’ half-power beam width for the five lowest tilt angles (0.5, 1.0, 1.5, 2.0, and 2.5◦) at the wind farm, assuming standard propagation con-ditions From Fig 1 it is seen that all wind turbines are in

Before

10 20 30

After (b)

〈 Z 〉 (dBZ)

−25

−20

−15

−10

Difference

(c)

〈 Z 〉 −Z0 (dB)

0 3 6 9 12

(d)

Before

10 20 30

After

(e)

〈 |V| 〉 (m s−1)

4.0 5.0 6.0 7.0 8.0

Difference

(f)

〈 |V| 〉 −V0 (m s−1)

−3.0

−2.0

−1.0 0.0 1.0 2.0

(g)

Azimuth ( ° )

Before

40 45 50 10

20 30

Azimuth ( ° )

After (h)

40 45 50

〈 W 〉 (m s−1)

1.6 1.8 2.0 2.2 2.4

Azimuth ( ° )

Difference

(i)

40 45 50

〈 W 〉 −W0 (m s−1)

−0.2 0.0 0.2 0.4

Figure 2 The columns to the left and in the middle show average reflectivity, hZi; average absolute radial velocity, h|V |i; and average

spec-trum width, hW i, before and after the construction of the Brunsmo wind farm The right-hand column shows the difference (after−before) The locations of the wind turbines are shown with black or white circles The impact of the wind turbines is seen for all spectral moments as changes to their average value The impact of the wind turbines extends to radar cells both cross- and downrange from the wind farm

the radar line of sight for the scan with the lowest tilt angle

(θ = 0.5◦) Three of the five wind turbines are located within

the same radar cell (azimuth gate 52, near 44◦azimuth)

4 Methods and results

4.1 Wind turbine impact on a single radar scan

One way to investigate the impact of wind turbines on

Doppler weather radar data is to compare the average values

of the spectral moments before and after the construction of

a wind turbine The differences between these average values

provide an estimate of the impact of the wind turbine

Reflectivity, Z, and spectrum width, W , are well suited for

calculating average values, but radial velocity measurements,

V, can be either positive or negative, depending on the wind

direction relative to the radar Since we are interested in

find-ing an estimate of the wind turbine impact on V , the influence

of the wind direction was minimised by studying the absolute

radial velocity, |V |

The average values of the above-described spectral mo-ments (Z, |V |, and W ) were calculated before the construc-tion of the Brunsmo wind farm (January 2008–March 2010) and after the wind farm’s start of operations (May 2010– December 2013) In order to investigate the areal extent of the impact of the wind turbines, multiple radar cells (range: 4–38 km; azimuth: 35–53◦) in the vicinity of the Brunsmo wind farm were analysed using data from the scan with the lowest tilt angle (θ = 0.5◦)

Undetected reflectivity measurements (see Sect 2) were included when calculating the average value of Z since these measurements carry actual information However, as unde-tected measurements for V and W do not contain reliable information, such measurements were excluded when calcu-lating the average values of |V | and W Invalid measurements were excluded for all spectral moments

Figure 2a and b shows the average reflectivity, hZi, be-fore and after the construction of the Brunsmo wind farm, respectively Figure 2a shows that hZi was uniform over the whole analysed area (especially in azimuth) before the

con-Azimuth ( ° )

Before

(a)

40 45 50 5

10 15 20 25 30 35

Rel freq V

0.2 0.4 0.6

Azimuth ( ° )

After

(b)

40 45 50 5

10 15 20 25 30 35

Rel freq V

0.2 0.4 0.6

Azimuth ( ° )

Before

(c)

40 45 50 5

10 15 20 25 30 35

Rel freq W

0.2 0.4 0.6 0.8

Azimuth ( ° )

After

(d)

40 45 50 5

10 15 20 25 30 35

Rel freq W

0.2 0.4 0.6 0.8

Figure 3 Relative frequency of real (detected and valid) measurements of radial velocity, V , and spectrum width, W , before and after the

construction of the Brunsmo wind farm The locations of the wind turbines are shown with black or white circles The wind turbines are seen

to increase the frequency of real measurements of V and W , both at the location of the wind turbines as well as cross- and downrange from the wind farm

struction of the wind farm, with only small variations in

am-plitude However, after the construction of the wind farm

Fig 2b shows that hZi increases in amplitude, not only in

the radar cells in which the wind turbines are located but also

in several radar cells downrange of the wind turbines One of

the highest values of hZi is seen in the radar cell in which

three wind turbines are located The average reflectivity in

this radar cell is hZi ≈ −6 dBZ, which should be compared

to hZi ≈ −18 dBZ in the same radar cell before the wind

tur-bines were built For convenience, Fig 2c shows the

differ-ence between hZi after and before the construction of the

wind farm

Tails of increased reflectivity downrange of wind turbines

have been noted in several other works (see, e.g., Crum et al.,

2008; Isom et al., 2009; Haase et al., 2010; Vogt et al., 2011;

Norin and Haase, 2012) Such tails are believed to be caused

by multiple scattering effects (scattering between multiple

turbines and/or scattering between turbine and ground) (Isom

et al., 2009; Vogt et al., 2011; Kong, 2014) The tails of

in-creased reflectivity seen in Fig 2b and c extend more than

20 km downrange of the wind turbines The amplitude of hZi

in the tails is seen to reach a maximum shortly behind the

wind turbines, after which it decreases with increasing

dis-tance

Figure 2d and e shows the average absolute radial

veloc-ity, h|V |i, before and after the construction of the wind farm,

respectively Before the construction of the wind farm it is

seen from Fig 2d that the amplitude of h|V |i increases with range from the radar but is very homogeneous in azimuth Figure 2e shows that after the wind farm became opera-tional the amplitude of h|V |i increased in radar cells con-taining wind turbines However, radar cells downrange from the wind turbines show a decrease in amplitude The largest value of h|V |i is found in the radar cell containing three wind turbines, where h|V |i > 8.5 m s− 1 In the radar cell be-hind the three turbines the smallest value of h|V |i is found,

h|V |i ≈3 m s−1 Before the construction of the wind farm the values in both these radar cells were h|V |i ≈ 6 m s−1 Fig-ure 2f shows the difference between h|V |i after and before the construction of the wind farm

Figure 2g and h shows the average spectrum width, hW i, before and after the construction of the wind farm, respec-tively In these figures it can be seen that after the con-struction of the wind farm a slight increase in hW i appears

in the radar cells containing wind turbines, whereas a de-crease in hW i occurs over a large area cross- and downrange

of the wind turbines The average spectral width increased from hW i ≈ 2.0 m s− 1 to hW i > 2.5 m s− 1 at the wind tur-bines, whereas behind the turbines a decrease down to hW i ≈ 1.8 m s− 1can be seen Decreased levels of hW i can be seen

up to 20 km behind the wind turbines The difference be-tween hW i after and before the construction of the wind farm

is shown in Fig 2i

Azimuth ( ° )

Before

(a)

2 4 6 8

〈 Z 〉 −Z0 (dB)

0 2 4 6 8 10

Azimuth ( ° )

After

(b)

2 4 6 8

〈 Z 〉 −Z0 (dB)

0 2 4 6 8 10

Azimuth ( ° )

Before

(c)

2 4 6 8

〈 |V| 〉 −V0 (m s−1)

−1.0 0.0 1.0 2.0

Azimuth ( ° )

After

(d)

2 4 6 8

〈 |V| 〉 −V0 (m s−1)

−1.0 0.0 1.0 2.0

Azimuth ( ° )

Before

(e)

2 4 6 8

〈 W 〉 −W

0 (m s−1)

−0.5 0.0 0.5 1.0

Azimuth ( ° )

After

(f)

2 4 6 8

〈 W 〉 −W

0 (m s−1)

−0.5 0.0 0.5 1.0

Figure 4 Difference in average reflectivity, hZi − Z0; difference in average absolute radial velocity, h|V |i − V0; and difference in average

before the construction of the wind farm For every scan, the data shown were taken from the range bin corresponding to the location of the

used since for these scans the range resolution is 2 times that of the scans with lower tilt angles The locations of the wind turbines are shown

on the bottom of each plot as black or white vertical lines The wind turbines are only in the radar line of sight for the scan with the lowest tilt angle but are nevertheless seen to have an impact on scans with higher tilt angles

The average values of V and W are based on real

mea-surements, i.e measurements that are neither undetected nor

invalid In addition to their average values it is also of

inter-est to study their frequency of occurrence Complementary

to the results presented in Fig 2 the relative frequency of

oc-currence of V and W is shown in Fig 3

Figure 3a and b shows the relative frequency of

occur-rence of V before and after the construction of the Brunsmo

wind farm, respectively By comparing the two figures, it is

seen that after the wind farm was constructed the relative

fre-quency of detected radial velocity measurements increased

from approximately 40 % to more than 70 % behind the wind

turbines

Figure 3c and d shows the relative frequency of occurrence

of W before and after the construction of the Brunsmo wind farm, respectively It is seen that the presence of the wind farm led to spectral width being detected more often The relative frequency of occurrence of W increased from ap-proximately 50 % to more than 90 %, at and behind the wind turbines

Together, Figs 2 and 3 show that the construction of the Brunsmo wind farm has led to real (detected) measurements

of all spectral moments occurring more frequently The av-erage value of Z increased at and near the wind turbines, whereas h|V |i and hW i increased in radar cells located at the wind turbines but decreased behind

4.2 Wind turbine impact on polar volume data

As was shown in Fig 1, the wind turbines in the Brunsmo

wind farm are in the radar line of sight for the scans with

the lowest tilt angle (θ = 0.5◦) However, this calculation is

based on the assumption of standard atmospheric conditions

and further assumes that the extent of the radar lobe is limited

by its half-power beam width In order to investigate whether

scans with higher tilt angles also are affected by the Brunsmo

wind farm, data from all 10 scans in the polar volume were

analysed

Figure 4 shows the impact of the wind farm on hZi, h|V |i,

and hW i for all 10 scans in the polar volume In Fig 4

ev-ery scan is represented by the radar cells in which the wind

turbines would be located if a vertical line from the

tur-bines were drawn from the ground For the higher tilt angles

(2.5◦≤θ ≤40◦) the average values of the spectral moments

from the two radar cells nearest to the wind turbines were

used, since for these scans the range resolution is 2 times

that of the lower scans (cf Table 1) Furthermore, in order

to clearly display the change in the spectral moments for all

scans in the same figure, the mean value in azimuth (for the

extent of the analysed area, 35–53◦) for every spectral

mo-ment from before the construction of the wind farm were

subtracted from the measurements (both before and after the

construction of the wind farm) These mean values are

de-noted by Z0, V0, and W0

Figure 4a and b shows hZi − Z0before and after the

con-struction of the wind farm, respectively Figure 4a shows that

before the wind farm was built hZi − Z0was homogeneous

in azimuth for all scans In Fig 4b, after the construction of

the wind farm, an increase in hZi − Z0 can be seen in the

radar cells near the location of the wind turbines for some

scans For the scan with the lowest tilt angle (θ = 0.5◦) the

increase is approximately 12 dB (cf Fig 2b) However,

in-creased levels of hZi − Z0 are seen not only in the lowest

scan (in which the wind turbines are in the radar line of sight)

but also in higher scans From Fig 4b it is seen that the fifth

scan (θ = 2.5◦) shows an increase of hZi−Z0≈8 dB, which

is much larger than that of the fourth scan (θ = 2.0◦), where

hZi − Z0≈2 dB This can partly be explained by the change

in radar cell resolution that occurs between the four lowest

scans and the six highest scans (cf Sect 2 and Table 1) and

is discussed further in Sect 5 A slight increase in hZi − Z0

(approximately 2 dB) still exists near 3 km altitude

Figure 4c and d shows h|V |i − V0 before and after the

construction of the wind farm, respectively Before the wind

farm was built, h|V |i − V0 was uniform in azimuth for all

scans, as seen in Fig 4c Figure 4d shows that after the wind

farm was constructed an increase in h|V |i − V0exists in the

radar cells near the wind turbines for the scans with the two

lowest tilt angles (θ = 0.5◦ and θ = 1.0◦) The largest

in-crease in h|V |i − V0is seen in the scan with the lowest tilt

angle, where the increase is close to 2.5 m s−1 For higher

tilt angles no change (θ = 1.5◦ and θ = 2.0◦) or a decrease

(2.5◦≤θ ≤14◦) in h|V |i−V0is seen A decrease of approx-imately −1.5 m s− 1can still be seen near 3 km altitude, far above the wind farm

Figure 4e and f shows hW i − W0before and after the con-struction of the wind farm, respectively As for the other two examined spectral moments, hW i − W0 is homogeneous in azimuth for all scans before the construction of the wind farm (see Fig 4e), whereas increased amplitudes in hW i−W0 are seen in Fig 4f, after the wind farm was built The in-crease in hW i − W0 for the second-lowest scan (θ = 1.0◦)

is close to 1.0 m s−1, higher than the increase for the lowest scan (θ = 0.5◦), which is near 0.5 m s−1 A sharp increase in

hW i−W0can be seen between the fourth scan (θ = 2.0◦) and the fifth scan (θ = 2.5◦), where the change in radar cell reso-lution occurs Increased values of hW i − W0can be seen far above the wind farm, near 3 km altitude

Figure 5 shows a cross section in range (4–38 km) and height (0–4 km) of the polar volume for azimuth gate 52, the gate in which three wind turbines are located (near 44◦ azimuth) The same quantities as in Fig 4 are shown (i.e

hZi − Z0, h|V |i − V0, and hW i − W0)

Figure 5a and b shows hZi − Z0before and after the con-struction of the wind farm, respectively In Fig 5b it is seen that, after the construction of the wind farm, increased val-ues of hZi − Z0extend tens of kilometres downrange of the wind turbines for the lowest two tilt angles (θ = 0.5◦ and

θ =1.0◦); cf Fig 2b For higher tilt angles no increase in

hZi − Z0downrange of the wind turbines can be seen Figure 5c and d shows h|V |i − V0before and after the con-struction of the wind farm, respectively Figure 5d shows that, after the wind farm was constructed, increased values

of h|V |i − V0exist in the radar cells in which the wind tur-bines are located for the lowest two tilt angles (θ = 0.5◦and

θ =1.0◦) Downrange of the wind turbines for these tilt an-gles a decrease in h|V |i − V0is seen For higher tilt angles (2.5◦≥θ ≤14◦) a decrease in hV i − V0exists at the location

of the wind turbines

Figure 5e and f shows hW i − W0before and after the con-struction of the wind farm, respectively Figure 5f shows that, after the construction of the wind farm, hW i−W0increased at and above the locations of the wind turbines, for altitudes up

to 3 km Downrange of the wind turbines a slight decrease in

hW i−W0is seen for the lowest tilt angle (θ = 0.5◦), whereas

a slight increase in hW i − W0can be seen for θ = 1.0◦ Supplementary to Figs 4 and 5, animations of hZi, h|V |i, and hW i for all 10 scans are shown in Figs S1–S3 in the Sup-plement, respectively These animations show a 3-D view of the impact the Brunsmo wind farm has on the three spectral moments From the animations it is seen that tails of changed amplitudes of the spectral moments are only visible for the scans with the lowest two tilt angles

Range (km)

Before

(a)

0 1 2 3 4

〈 Z 〉 −Z0 (dB)

−2 0 2 4 6 8

Range (km)

After

(b)

0 1 2 3 4

〈 Z 〉 −Z0 (dB)

−2 0 2 4 6 8

Range (km)

Before

(c)

0 1 2 3 4

〈 |V| 〉 −V

0 (m s−1)

−3

−2

−1 0

Range (km)

After

(d)

0 1 2 3 4

〈 |V| 〉 −V

0 (m s−1)

−3

−2

−1 0

Range (km)

Before

(e)

0 1 2 3 4

〈 W 〉 −W

0 (m s−1)

0.0 0.2 0.4 0.6 0.8

Range (km)

After

(f)

0 1 2 3 4

〈 W 〉 −W

0 (m s−1)

0.0 0.2 0.4 0.6 0.8

Figure 5 Difference in average reflectivity, hZi − Z0; difference in average absolute radial velocity, h|V |i − V0; and difference in average

azimuth) The locations of the wind turbines are shown on the bottom of each plot as black vertical lines The wind turbines are only in the radar line of sight for the scan with the lowest tilt angle but are nevertheless seen to impact scans with higher tilt angles

4.3 Wind turbine impact on a single radar cell

In Sects 4.1 and 4.2 average values of the spectral

mo-ments were compared before and after the construction of

the Brunsmo wind farm While this is a robust and simple

way to illustrate the impact of wind turbines on weather radar

data, these average values do not separate the weather signal

from the unwanted wind turbine clutter Hence, this method

tacitly assumes that the weather signal, on average, was

simi-lar during the two measurement periods (before and after the

construction of the wind farm)

In order to perform a more in-depth analysis of the impact

of wind turbines on radar data, one would ideally want to

know the actual, unaffected values of the weather signal at

all times A way to simulate this is to use simultaneous

mea-surements from a reference radar cell, a radar cell unaffected

by the wind turbines

This technique was used by Haase et al (2010) and Norin and Haase (2012) in their works As reference cells they used radar cells with the same location in range and azimuth as the wind-turbine-affected radar cells, albeit from a scan with

a higher tilt angle (θ = 2.0◦) Furthermore, in order to re-move the influence of weather, they chose to select only those measurements for which the reflectivity in the reference cell was undetected (i.e Zref= −30 dBZ) As can be seen from Fig 4, such a choice of reference radar cells must be treated with caution since radar cells in scans from higher tilt angles may also be affected by the presence of the wind farm

In this work a different choice of reference radar cell was used: the radar cells one radar cell up-range from the radar

Z (dBZ)

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15

Z

Z

Z

Z

Z

Z

Z

Z

Figure 6 Relative frequency distributions of reflectivity from a

The grey and white backgrounds represent the bins that were used

to create the distributions

cells in which the wind turbines are located From Fig 2 it is

seen that these radar cells are not affected by the wind farm

In order to investigate the impact of wind turbines on a

sin-gle radar cell, we chose to study data from the radar cell in

which three wind turbines are located (θ = 0.5◦, range cell 7,

azimuth gate 52) The corresponding reference radar cell was

selected from the scan with the same tilt angle and azimuth

gate albeit one range bin up-range from the

wind-turbine-affected cell (θ = 0.5◦, range cell 6, azimuth gate 52)

In the analysis frequency distributions of the spectral

mo-ments (Z, V , and W ) were examined as functions of Zref In

order to have sufficiently many samples for the analysis, data

for Z and V were sorted into 35 bins

For Z, one bin was used to count all measurement for

which Z = −30 dBZ (undetected measurements) and one bin

counted all invalid measurements The remaining 33 bins

were equally spaced from Z = −29.6 dBZ to Z = 71.6 dBZ

For V , one bin was used to count all undetected

measuments and one bin counted all invalid measuremeasuments The

re-maining 33 bins were equally spaced from V = −24 m s−1

to V = 24 m s−1

Since measurements of W only consist of four different

classes (see Sect 2) and have separate representations of

un-detected and invalid measurements, data for W were used as

they are

Let us first examine the validity of the choice of reference radar cell Figure 6 shows relative frequency distributions of reflectivity from the reference cell, Zref, and from the wind-turbine-affected radar cell, Zwt, before and after the construc-tion of the Brunsmo wind farm, using data from the scan with the lowest tilt angle (θ = 0.5◦) From Fig 6 it is seen that the distributions of Zref, both before and after the construction

of the wind farm, are similar to the distribution of Zwtfrom before the wind farm was built Some small differences exist between these distributions, but they are minor when com-pared to the distribution of the Zwt after the construction of the wind farm, which is dominated by a prominent peak near

Z ≈5 dBZ

From Fig 6 it is seen that neither Zrefnor Zwtis normally distributed This means that the average value of Z, used in Sect 4.1 and Sect 4.2, does not coincide with the value of Z

at the peak of the frequency distribution

Distributions of reflectivity from scans with higher tilt an-gles, using the same choice for reference radar cells (the radar cells one radar cell up-range from the wind-turbine-affected cells), all show similar behaviour The chosen ref-erence radar cells were therefore judged to provide a good (albeit not perfect) representation of the weather signal in the wind-turbine-affected radar cells

Having validated the choice of reference radar cell, a more in-depth analysis of the wind-turbine-affected radar cell from the scan with the lowest tilt angle (θ = 0.5◦) could be per-formed To analyse the impact of the wind turbines, fre-quency distributions of the spectral moments from the wind-turbine-affected radar cell (Zwt, Vwt, and Wwt) were created

as a function of the simultaneous reflectivity measurements from the reference radar cell (Zref) In Fig 7 the relative fre-quency distributions of Zwt, Vwt, and Wwtare shown Figure 7a shows relative frequency distributions of Zwt

as a function of Zrefbefore the wind farm was constructed

It is seen that, as expected, the measurements of Zref in general accurately represent the measurements of Zwt For

Zref.−15 dBZ the values of Zwttend to be somewhat higher than Zref(cf Fig 6) In Fig 7b the same relative frequency distributions are shown, albeit this time for data gathered after the construction of the wind farm For Zref&5 dBZ

it is seen that Zref provides a good representation of Zwt, whereas for Zref.5 dBZ the situation is different For all

val-ues of Zref.5 dBZ the distributions of Zwt exhibit a peak

at Zwt≈5 dBZ This reflectivity value, Z ≈ 5 dBZ, is the most frequent reflectivity value generated by the wind tur-bines When the reflectivity value from the actual weather is smaller than this value, the wind turbines effectively hide the weather signal When the weather signal is larger than the wind turbine clutter, the reflectivity value approaches that of the reference cell

Figure 7c shows the relative frequency distributions of

Vwt as a function of Zref before the wind farm was con-structed From Fig 7c it is seen that the distributions of Vwt have their maxima near Vwt≈ ±5 m s−1, regardless of the

Zwt (dBZ)

Zref

Before

(a)

−30 −15 0 15 30

−30

−15 0 15

0.1 0.2 0.3 0.4

Zwt (dBZ)

Zref

After

(b)

−30 −15 0 15 30

−30

−15 0 15

0.1 0.2 0.3 0.4

Vwt (m s−1)

Zref

Before

(c)

−20 −10 0 10 20

−30

−15 0 15

0.04 0.08 0.12

Vwt (m s−1)

Zref

After

(d)

−20 −10 0 10 20

−30

−15 0 15

0.04 0.08 0.12

Wwt (m s−1)

Zref

Before

(e)

0−1 1−2 2−3 >3

−30

−15 0 15

0.2 0.4 0.6

Wwt (m s−1)

Zref

After

(f)

0−1 1−2 2−3 >3

−30

−15 0 15

0.2 0.4 0.6

Figure 7 Relative frequency distributions of reflectivity, Zwt; radial velocity, Vwt; and spectrum width, Wwt, from a radar cell in which three

the construction of the wind farm look different

value of Zref Figure 7d shows the same distributions,

al-beit for data recorded after the construction of the wind farm

For Zref&5 dBZ the distributions of Vwt are similar to those

shown in Fig 7c, but for smaller values of Zrefthe

distribu-tions of Vwtlook different For Zref.5 dBZ the distributions

of Vwtall have their maxima at Vwt≈0 m s−1 Much as for

Zwt, for Zref&5 dBZ the distributions of Vwt approach the

corresponding distributions with data from before the

con-struction of the wind farm

For Zref.5 dBZ, the frequency distribution of Vwt was

spread over almost all velocity bins, resulting in an increase

in h|Vwt|i However, when extending the analysis to radar

cells downrange of the wind turbines, it was found that the

frequency distribution of Vwt was concentrated to the

low-velocity bins, resulting in a decrease in h|Vwt|i A possible reason for this is discussed in Sect 5

For comparison a wind rose for the period of study (2008– 2013), together with the distribution of wind speed, is shown

in Fig 10 The measurements of wind speed and wind di-rection for this figure come from an automatic weather sta-tion (56.2619◦N, 15.2742◦E), located approximately 21 km

to the west of the weather radar The wind speed measure-ments have a resolution of 1 m s− 1and were available at most once per hour during the period of study

Figure 7e shows the relative frequency distributions of

Wwt as a function of Zref before the wind farm was con-structed From Fig 7e it is seen that the distributions of Wwt vary depending on the value of Zref For Zref.−15 dBZ, the

distributions of Wwt peak for Wwt=0–1 m s−1, whereas for